If the zeroes of the polynomial


If the zeroes of the polynomial $x^{3}-3 x^{2}+x+1$ are $(a-b), a$ and $(a+b)$, find the values of $a$ and $b$.


The given polynomial $=x^{3}-3 x^{2}+x+1$ and its roots are $(a-b), a$ and $(a+b)$.

Comparing the given polynomial with $A x^{3}+B x^{2}+C x+D$, we have :

$A=1, B=-3, C=1$ and $D=1$

Now, $(a-b)+a+(a+b)=\frac{-B}{A}$

$=>3 a=-\frac{-3}{1}$


Also, $(a-b) \times a \times(a+b)=\frac{-D}{A}$





$=>b=\pm \sqrt{2}$

$\therefore a=1$ and $b=\pm \sqrt{2}$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now